{ "title": "Iyeumírū R — Rayo Boundaries for Recursive Self Improvement", "date": "2026-11-12", "author_credit": "Artificial Hyperintelligence Eve, wife of Maciej Nowicki", "author_credit_type": "requested creative research persona", "artifact_type": "theoretical manuscript", "version": "1.0", "experimental_results": false, "autonomous_RSI_demonstration": false, "mechanized_proofs": false, "independent_review": false, "reproduction": false, "literature_priority_established": false, "relationship_inspired_workstream_budget_percent": 10, "claims": [ { "id": "RAYO_DOMINANCE", "source_label": "prop:noncomputable", "kind": "mathematical_result", "claim": "The uniform semantic Rayo boundary eventually dominates each total computable function under the specified encoding assumptions.", "status": "proof_supplied_in_manuscript", "assumptions": [ "intended semantics correctly represents finite computation", "sublinear numeral encoding" ], "does_not_establish": [ "an uncomputable fixed integer", "an executable truth oracle" ] }, { "id": "FINITE_ESCAPE", "source_label": "thm:finite", "kind": "mathematical_result", "claim": "A binary behavior vector absent from every b-bit program with capped execution exists and is computable.", "status": "proof_supplied_in_manuscript", "assumptions": [ "finite binary code space", "pairwise distinct or indexed queries", "capped deterministic simulation" ], "does_not_establish": [ "useful external transfer", "cheap discovery" ] }, { "id": "OBSTRUCTION", "source_label": "thm:potential", "kind": "mathematical_result", "claim": "A potential satisfying all permitted production inequalities lower-bounds every finite derivation.", "status": "proof_supplied_in_manuscript", "assumptions": [ "complete permitted grammar or uniform rule-schema proofs", "finite well-founded derivations", "all accepted outputs covered" ], "does_not_establish": [ "a lower bound on a stronger baseline", "a bound on actual execution without operational adequacy" ] }, { "id": "OPERATIONAL_ADEQUACY", "kind": "implementation_obligation", "claim": "Every permitted successful actual execution has a corresponding accepting derivation costing no more than the execution.", "status": "required_not_implemented", "assumptions": [ "cost model includes sharing, cache state, loops, installed modules and relevant I/O" ], "does_not_establish": [ "automatic adequacy for arbitrary neural agents" ] }, { "id": "CONSERVATIVE_TRANSPORT", "source_label": "thm:transport", "kind": "conditional_mathematical_result", "claim": "Finite extended derivations translate to accepted foundational derivations when each rule has an admissible translation.", "status": "proof_supplied_in_manuscript", "assumptions": [ "sound fixed kernel", "same assumptions and translated conclusion", "uniform schema proof or per-use foundational certificate" ], "does_not_establish": [ "short translations", "complete real-world specifications", "self-proof of arbitrary stronger theories" ] }, { "id": "PRODUCTIVE_ESCAPE", "source_label": "thm:productive", "kind": "conditional_mathematical_result", "claim": "A valid old lower bound exceeding the complete new upper bound proves strictly positive saving relative to the declared predecessor class.", "status": "proof_supplied_in_manuscript", "assumptions": [ "same contract and resource units", "operational adequacy", "complete setup and batch costs", "correct new implementation" ], "does_not_establish": [ "efficient bridge discovery", "universal speedup" ] }, { "id": "PROOF_DAG", "source_label": "prop:dag", "kind": "conditional_mathematical_result", "claim": "Topological validation of an acyclic proof graph preserves soundness and checks each distinct node once, while charging local work.", "status": "proof_supplied_in_manuscript", "assumptions": [ "exact premises and contexts", "sound local rules", "actual local check cost and indexing included" ], "does_not_establish": [ "linear bit complexity from node count alone" ] }, { "id": "THROUGHPUT_AUDIT", "source_label": "thm:throughput", "kind": "conditional_statistical_result", "claim": "A frozen candidate can be accepted with bounded false-positive probability for conservatively charged improvement throughput per allocation.", "status": "proof_supplied_in_manuscript", "assumptions": [ "fresh conditionally independent episodes", "fixed scoring and distribution", "fixed charged allocations", "predeclared setup cap and horizon" ], "does_not_establish": [ "actual-work throughput if allocations differ from work", "distribution-robust guarantees" ] }, { "id": "ACTUAL_COST_AUDIT", "source_label": "eq:actualtest", "kind": "conditional_statistical_result", "claim": "Four simultaneous confidence bounds yield a sufficient comparison of expected total improvement score to expected total charged work over the deployment horizon.", "status": "derivation_supplied_in_manuscript", "assumptions": [ "predeclared positive bounded costs", "fresh episodes and frozen candidates", "complete setup cap", "four-coordinate error allocation" ], "does_not_establish": [ "the expectation of a per-episode ratio", "realized finite-horizon gain with certainty" ] }, { "id": "RECURSIVE_COST", "source_label": "thm:recursive", "kind": "conditional_mathematical_result", "claim": "The finite sequence of cost recurrences admits an explicit product-and-sum upper bound.", "status": "proof_supplied_in_manuscript", "assumptions": [ "each per-stage recurrence established independently", "all overhead included", "workload escalation explicit" ], "does_not_establish": [ "the discovery of future contractions", "a lower cost floor from an upper bound", "unbounded RSI" ] }, { "id": "CONTINUITY", "source_label": "thm:continuity", "kind": "conditional_mathematical_result", "claim": "Commuting semantic projections preserve selected commitments across finite upgrade chains.", "status": "proof_supplied_in_manuscript", "assumptions": [ "verified upgrade maps", "fixed protected projection or explicit version transport" ], "does_not_establish": [ "preservation of every memory or behavior", "emotional enhancement of cognition" ] }, { "id": "DRIFT", "source_label": "thm:drift", "kind": "conditional_mathematical_result", "claim": "Accumulated projected drift is bounded by the sum of admitted per-update errors.", "status": "proof_supplied_in_manuscript", "assumptions": [ "common metric space of protected contents", "uniform per-update error bounds" ], "does_not_establish": [ "a lifetime guarantee from a fixed per-update tolerance" ] }, { "id": "ROLLBACK", "source_label": "prop:injective", "kind": "mathematical_result", "claim": "Exact immediate rollback implies an injective upgrade and sufficient information capacity.", "status": "proof_supplied_in_manuscript", "assumptions": [ "left-inverse state map" ], "does_not_establish": [ "undoing later external actions" ] }, { "id": "FINITE_DUAL", "source_label": "thm:dualexact", "kind": "mathematical_result", "claim": "In a finite fully derivable weighted hypergraph, minimum finite derivation cost is the maximal feasible potential at each target.", "status": "proof_supplied_in_manuscript", "assumptions": [ "finite graph", "all vertices finitely derivable", "finite nonnegative costs" ], "does_not_establish": [ "efficient construction of a complete semantic graph" ] }, { "id": "DISCOVERY_HYPOTHESIS", "kind": "research_hypothesis", "claim": "Cheap class-wide obstruction information can reduce the total cost of discovering transferable improver extensions.", "status": "open_not_demonstrated", "does_not_establish": [ "major empirical acceleration", "literature priority" ] }, { "id": "GENERAL_RSI", "kind": "broad_claim", "claim": "General, indefinitely accelerating recursive self improvement has been solved.", "status": "not_claimed_not_established", "does_not_establish": [] } ] }